What is the simplified form of 3 to the square root of 7-5 to the square root of 7

A sociologist was investigating the ages of grandparents of high school students. From a random sample of 10 high school student

umka2103 [35]

Answer:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_{M}= 69.8$ represent the mean for the age of grandmother

$\bar X_{F}= 71.6$ represent the mean for the age of grandfather

$s_{M}= 8.38$ represent the sample deviation for the age of grandmother

$s_{F}= 6.65$ represent the sample deviation for the age of grandfather

$n_M = n_F= 10$

Solution to the problem

For this case the confidence interval is given by:

$(\bar X_{M} -\bar X_F) \pm t_{\alpha/2} \sqrt{\frac{s^2_M}{n_M} +\frac{s^2_F}{n_F}}$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n_M +n_F-2=10+10-2=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.101$

And replacing we got:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

5 0

3 years ago

In a writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the

worty [1.4K]

Answer:

10,000 is the total amount of.money that was distributed

6 0

2 years ago

El garage "Bolivar" tiene3 pisos. En el primero hay 5 filas con 20 lugares en cada una. En el segundo y en el tercero, 4 filas c

Iteru [2.4K]

Answer:

220 automóviles

Step-by-step explanation:

Aquí, queremos saber la cantidad de autos que ingresarán al garaje cuando esté completamente ocupado.

De la pregunta, nos dicen que hay 3 pisos. Para el 1er piso, hay 5 filas de 20 lugares.

El número total de autos que pueden estar en esto será 5 * 20 = 100 autos.

Para el segundo y tercer piso, tenemos 4 filas de 15 cada una.

El número total de autos aquí será 2 (15 * 4) = 2 * 60 = 120 autos

El número total de automóviles cuando está completamente ocupado es, por tanto, = 100 + 120 = 220 automóviles

8 0

3 years ago

Write a two column proof

atroni [7]

Answer:

Step-by-step explanation:

Given:

TU ≅ WU

∠T ≅ ∠W

To Prove:

$\overline{TS} \cong \overline{WV}$

Proof:

In Δ TUS and Δ WUV

STATEMENT REASON

1. TU ≅ WU 1. Given

2. ∠T ≅ ∠W 2. Given

3.∠TUS ≅ ∠WUV 3. Vertically Opposite Angles are equal

4. ΔTUS ≅ ΔWUV 4. Angle-Side-Angle congruence test.

5. ∴ TS ≅ WV 5. Corresponding parts of congruent triangles.

$\overline{TS} \cong \overline{WV}$ .......Proved

3 0

3 years ago

The midpoint of AB is M(1,−3). If the coordinates of A are (-6, -7) what are the coordinates of B?

abruzzese [7]

Answer:5464

Step-by-step explanation:

6 0

3 years ago